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- W2748841261 abstract "Shape from Equal Thickness Contours G. Cong and B. Parvin Information and Computing Sciences Division Lawrence Berkeley National Laboratory Berkeley, CA 94720 April 4, 2001 Abstract A unique imaging modality based on Equal Thickness Contours (ETC) has introduced a new opportunity for 3D shape reconstruction from multiple views. We present a computational framework for representing each view of an object in terms of its object thickness, and then integrat- ing these representations into a 3D surface by algebraic re- construction. The object thickness is inferred by grouping curve segments that correspond to points of second deriva- tive maxima. At each step of the process, we use some form of regularization to ensure closeness to the original features, as well as neighborhood continuity. We apply our approach to images of a sub-micron crystal structure ob- tained through a holographic process. or no depth information. In contrast, electron holography– with coherent illumination–provides both magnitude and phase information that can be used to infer object thickness in terms of ETCs from each view of the sample. The holo- graphic images contain interference fringes with spacings, in the best case down to less than an angstrom, where in- terference is between the transmitted and diffracted beams. Similar imaging technique includes satellite radar inter- ferometry, where the phase difference between two radar returns–at two different times–from the same spatial loca- tion is used for change detection [9]. It has been demon- strated that minute geological changes (as a result of earth- quake or movement in the earth’s crust) can be recovered with this approach. A simulation of ETCs for a synthetic object is shown in Figure 1. The main issue is that this mode of representa- tion is inherently ambiguous since objects with completely different geometry can produce similar ETCs, as shown in Figure 2. Thus, multiple views of an object is essential for 3D shape recovery. In practice, however, these images may have low contrast, be noisy, contain artifacts, and may have shading; as a result, it is difficult to compute closed contours from these fringe patterns. Figure 3 shows three views of a real crystal structure that will be used for shape recovery. There is a small angle of rotation between differ- ent views, as reflected by the changes in the fringe patterns. Our method for shape recovery consists of five steps, some of which build on existing techniques developed in the computer vision community. The protocol for shape recovery is shown in Figure 4. Dominant features in these images are roof edges corresponding to crease lines; how- ever, it is well-known that it is difficult to extract these fea- tures directly in the presence of scale-change and noise. Here, we have adopted a stepwise refinement of images to extract a desirable representation. The first step of the pro- cess enhances peaks and valleys of the original data with adaptive smoothing. Next, crease points are extracted and grouped on the basis of collinearity and convexity. It is assumed that grouping does not produce closed contours, 1 Introduction The problem of shape-from-X has been a central research topic in the computer vision community. These include– but are not limited to–shape from shading [4, 11], texture [8], contour [14], color [2, 1], etc. These techniques have been applied from images obtained in controlled environ- ments to natural outdoor scenes that may include more than one view. In this paper, we introduce a new imag- ing modality, and the corresponding method for shape re- covery that has not yet been addressed by the computer vi- sion community. This is based on equal thickness contour (ETC), which is obtained through a holographic process. One imaging source example is holographic electron mi- croscopy of sub-micron crystal structures. Conventional electron microscopy presents projected images with little This work is supported by the Director, Office of Energy Research, Office of Computation and Technology Research, Mathematical, In- formation, and Computational Sciences Division, and Office of Basic Energy Sciences, Material Sciences Division of the U. S. Department of Energy under contract No. DE-AC03-76SF00098 with the Univer- sity of California. The LBNL publication number is 41678. E-mail: gcong@media.lbl.gov or parvin@media.lbl.gov" @default.
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